Answer:
see explanation
Step-by-step explanation:
(1)
the sine of an angle = [tex]\frac{opposite}{hypotenuse}[/tex]
(a)
here the opposite is 12 and the hypotenuse is 13
12 is the side opposite ∠DEF ← required angle
(b)
the tangent of an angle = [tex]\frac{opposite}{adjacent}[/tex]
here the opposite is 5 and the adjacent is 12
∠DFE ← required angle
(2)
to calculate AB use Pythagoras' identity in the right triangle
AB² = 2² + 3² = 4 + 9 = 13, hence
AB = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to nearest tenth )
tanB = [tex]\frac{2}{3}[/tex] ⇒ B = 33.7°
tanA = [tex]\frac{3}{2}[/tex] ⇒ A = 56.3°
